Vol. 15, No. 2, 1965

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Monotone approximation

Oved Shisha

Vol. 15 (1965), No. 2, 667–671
Abstract

How close can one approximate a monotone function by a monotone polynomial of degree n, or a convex function by a convex polynomial of degree n? This leads to the following general question. Let k and n be given, and suppose a real fuction f satisfies f(k)(x) 0 throughout a closed, finite interval [a,b]. How close can one approximate f on [a,b] by a polynomial of degree n whose k-th derivative, too, is 0 there? We give an answer to the question.

Mathematical Subject Classification
Primary: 41.15
Milestones
Received: 17 March 1964
Published: 1 June 1965
Authors
Oved Shisha